Mixture Models
نویسنده
چکیده
Consider the task of summarizing the data in Figure 1. A common technique for performing this task is to use a statistical model known as a mixture model. Relative to many other models for estimating densities, mixture models have a number of advantages. First, mixture models can summarize data that contain multiple modes. In this sense, they are more powerful than distributions from the exponential family (e.g., Gaussian, binomial, Poisson, etc.). Second, mixture models are parametric models. Methods based on probability theory, such as maximum likelihood and Bayesian inference methods, are often easily applied to mixture models. Third, mixture models are parsimonious in the sense that they typically combine distributions that are simple and relatively well-understood. In the conventional statistics literature, the components of mixture models are nearly always members of the exponential family of distributions (but this has recently begun to change; we will talk about this more later in the semester).
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